Titlebook: Combinatorial and Algorithmic Aspects of Networking; 4th Workshop, CAAN 2 Jeannette Janssen,Pawe? Pra?at Conference proceedings 2007 Spring

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Cleaning Random ,-Regular Graphs with Brushes Using a Degree-Greedy Algorithmeven). We then use a differential equations method to find the (asymptotic) number of brushes needed to clean a random .-regular graph using this algorithm. As well as the case for general ., interesting results for specific values of . are examined. We also state various open problems.

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Vertex Pursuit Games in Stochastic Network Models random power law graphs. We investigate asymptotic results for the game of Cops and Robber played on .(.) and .(.,.). Under mild conditions on the degree sequence ., an asymptotic lower bound for the cop number of .(.) is given. We prove that the cop number of random power law graphs with . vertice

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Preemptive Scheduling on Selfish Machines agents. Our goal is to minimize the makespan, whereas the goal of the agents is to maximize their profit. We show that a known algorithm is monotone and can therefore be used to create a truthful mechanism for this problem which achieves the optimal makespan. We extend this result for additional co

CRAMP

Selfish Routing and Path Coloring in All-Optical Networks is, functions that charge a player according to her own strategy only..We first strengthen a known relation between such games and online routing and path coloring. In particular, we show that the price of anarchy of such games is lower-bounded by, and in several cases precisely equal to, the compe

Veneer

A Worst-Case Time Upper Bound for Counting the Number of Independent Setsr. Exploiting the strong relation between .(.) and Fibonacci numbers, we show that if the depth-first graph of . does not contain a pair of basic cycles with common edges, then .(.) can be computed in linear time (in the size of the graph). This determines new classes of instances of graphs without

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